We use a path-integral Monte Carlo method together with state-of-the-art pair and three-body potentials to calculate the third virial coefficient C(T) of para-hydrogen in the temperature range 30-2000 K. Our results point out that non-additive three-body interactions have a sizable effect in determining the value of C(T) for T < 200 K. Although a good agreement with experimental data is obtained, the accuracy of the calculations is limited by the incomplete knowledge of the three-body potential energy surface. (C) 2012 Elsevier B.V. All rights reserved.